Calculus of Variations and Geometric Measure Theory

A. Halavati

New weighted inequalities on two-manifolds

created by halavati on 10 Oct 2023
modified on 08 Apr 2025

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Submitted Paper

Inserted: 10 oct 2023
Last Updated: 8 apr 2025

Year: 2023

ArXiv: 2310.04868 PDF

Abstract:

We establish a new class of $L^2$-weighted elliptic estimates on smooth two-manifolds for a family of weights satisfying an equation with explicit constants. This family includes weights that are comparable to the product of positive powers of the geodesic distance to a given collection of points. Our primary motivation is to derive estimates related to a weighted Hodge decomposition for one-forms.


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